Question

2cos(theta) + 1 = 0

Answer 1

Are you solving for theta?

Answer 2

Hi,
first
the solution for cos angle is given by the expression
\[2n \pi \pm \alpha \]
\[where ( 0 < \alpha < 2\pi )\]

Now let's move to ur problem...
2cos(theta) + 1 = 0
cos(theta) = -(1/2)

u know that cos pi/3 = 1/2
then
according to the law cos (pi - theta ) = - cos theta (where theta < pi/2 )
cos (pi - pi/3) = - cos pi/3 = -(1/2)

now
cos(theta) = -(1/2)
cos(theta) = cos (pi - pi/3)

now apply the above equation here
\[\theta = 2n \pi \pm ( \pi - \frac{ \pi }{ 3 } )\] where n is an integer

these r the all posible vales for theta

Answer 3

I got up to cos(theta) = -(1/2) and then found -(1/2) on the unit circle for cosine which is 2pi/3 and 4pi/3 or 120 degrees and 240 degrees. But I feel that since I am using cosine and cosine cannot be in the negatives that one of the two answers that I found is incorrect. Please Explain?